We can use the te form with the group 1 verb しまう to express regret at an action.
【Verb: te Form】しまう
友達との約束をすっかりと忘れてしまう。
Completely forget about an appointment with a friend.
その時に冷静に考えていなくて、ひどいことをうっかりと言ってしまったよ。
I wasn’t thinking clearly at the time and I mindlessly said something horrible.
Note the te form is used with the present participle in the first clause.
家事をして、大事なものを捨てしまいました。
I did the house chores and accidentally threw out something important.
The word “accidentally” isn’t explicitly used in the above sentence, but the use of しまう suitably expresses the nuance of regret so it is fair to assume that you didn’t mean to throw the item away.
学生のうちに、ちゃんと勉強しなければ後悔してしまうよ。
If you don’t study hard while you’re a student you’ll come to regret it.
それをやっちゃってはいけないことだよ。
You’re not allowed to do that.
〜てしまう can only be used to express regret at an action has been or will be performed; it cannot be used with the negative te form to express regret at having not done something.
パーティで話した女の子に電話番号を聞かないでしまった。(✘)
[I wish I had asked the girl I spoke to at the party for her phone number.]
Instead we would use the conditional with the past tense of good to say, “it would be good if I had done x”.
パーティで話した女の子に電話番号を聞けばよかった。
I wish I had asked the girl I spoke to at the party for her phone number.
This structure can also be used to express completion; however, this is a more minor usage. In the vast majority of cases when you hear ～てしまう it will be to express regret.
お腹が空いていて、ケーキを三つ食べてしまった。
I was hungry and so finished three whole cakes.
飛行機で本を３冊読んでしまいました。
To read three books on the airplane.
In casual conversation you will often hear an altered form of 〜てしまう.
Verbs with the te form ending 〜て ⇒ ちゃう
Verbs with the te form ending 〜で ⇒ じゃう
どっかで財布をなくしちゃったみたい。
It seems I lost my wallet somewhere.
娘は毎日友達と遊んじゃってて、宿題とかは全然やらないのよ。
My daughter is hanging out with her friends every day.